Charged sphere

[jnuz73hbn]

Homework Statement

Hello guys,

Consider a spherical, electrically charged body with mass
and charge
, located next to a grounded conducting surface.
The interaction is modeled using the method of image charges.

(1)Determine the maximum radius for which the body is still held against
the surface by electrostatic attraction.

The charged spherical body is now freely suspended in air.
(2) Find out the critical electric field strength of air.
(3)Determine the minimum radius for which the electric field at the
surface of the body does not exceed

Relevant Equations

$$
F_{\mathrm{el}}=F_g
$$

$$
r_{\max}=\sqrt{\frac{kq^2}{4mg}}
$$

$$
E_{\mathrm{crit}}=3.0\times10^6\,\mathrm{V/m}
$$

$$
E(r_f\mid r_{\min})=E_{\mathrm{crit}}
$$





I think I'm missing something in the formulas

$$
r_{\max}=\sqrt{\frac{kq^2}{4mg}}
$$

$$
r_{\min}=\sqrt{\frac{k|q|}{E_{\mathrm{crit}}}}
$$

 

[kuruman]

Why do you think you are missing something in the formulas?

 

[jnuz73hbn]

Why do you think you are missing something in the formulas?

for the first I calculated this. Is that formula correct for r_max? Because 0,7m for a radius of a sphere is very big.
$$
r_{\max}
=
\sqrt{
\frac{
(8.99\times10^9\,\mathrm{N\,m^2/C^2})
(3.9\times10^{-7}\,\mathrm{C})^2
}{
4(2.8\times10^{-3}\,\mathrm{kg})(9.81\,\mathrm{m/s^2})
}
}
\approx 0.70\,\mathrm{m}
$$

 

[kuruman]

for the first I calculated this. Is that formula correct for r_max? Because 0,7m for a radius of a sphere is very big.
$$
r_{\max}
=
\sqrt{
\frac{
(8.99\times10^9\,\mathrm{N\,m^2/C^2})
(3.9\times10^{-7}\,\mathrm{C})^2
}{
4(2.8\times10^{-3}\,\mathrm{kg})(9.81\,\mathrm{m/s^2})
}
}
\approx 0.70\,\mathrm{m}
$$

Where did the numbers come from? You should post the problem exactly as was given to you. Also, these numbers that you show do not produce the answer that you quote. Redo the calculation, preferably on a spreadsheet, where you can easily troubleshoot what you are doing.

 

[jnuz73hbn]

Where did the numbers come from? You should post the problem exactly as was given to you. Also, these numbers that you show do not produce the answer that you quote. Redo the calculation, preferably on a spreadsheet, where you can easily troubleshoot what you are doing.

Given values are: q= 3.9 * 10^-7 C , m= 2,8 *10^-3 kg
$$
r_{\max}
=
\sqrt{
\frac{(3.9\times10^{-7})^2}
{16\pi(8.854\times10^{-12})(2.8\times10^{-3})(9.81)}
}
\approx
0.1115\,\mathrm{m}
$$